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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (1-50 of 97 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
320.84.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.84.2.b1.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.85.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.85.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.271.2.a1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.F_5$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.568.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.569.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.570.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.571.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.571.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.572.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.572.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.573.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.574.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.574.2.b1.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.575.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.575.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.576.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.576.2.b1.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.577.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.578.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.578.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.579.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.579.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.580.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.580.2.b1.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.581.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.582.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.583.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.584.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.586.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.588.2.c1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.836.2.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.837.2.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.837.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.838.2.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.839.2.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.840.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^3.D_{20}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.846.2.b1.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.846.2.b1.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.847.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.847.2.d1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.848.2.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.849.2.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.849.2.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.850.2.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.874.2.a1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.1152.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.1153.2.c1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
320.1154.2.b1 $C_2^3.D_{10}$ $2^{5} \cdot 5$ ✓ ✓ ✓ $C_2^4.D_{10}$ $2^{6} \cdot 5$ $C_2$ $2$ ✓
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